Caimans are South American alligators and no less intimidating than any other kind of alligator. Caiman spotting has become one of the not-to-miss Amazon activities (along with piranha fishing). You wait till dusk when the caimans are most active then go out on the river in a canoe and watch for their glinting eyes reflected in your torch light.
Most of the Amazons jungle lodges will offer caiman spotting as one of their activities, often with the additional excitement of the guide jumping into the river and wrestling the caiman on board your boat for you viewing pleasure.